Special Relativity (SR)

Albert Einstein’s miracle year, 1905, brought forth five scientific papers that changed the world forever. One of them, discussed previously, described the nature of light, and another proposed the theory of special relativity. This proclaimed that the speed of light was constant in all inertial reference frames and for all observers. This is an amazing statement that goes against our experience! Imagine you are in a car traveling 60 miles per hour. Assuming no wind resistance, if you lean out of the car and throw a baseball in your direction of motion, 30 miles per hour, the speed of the ball would be 30 miles per hour relative to you. But the speed of the baseball as measured by an observer on the side of the road would be 90 miles per hour (a great fast ball!). However, if you similarly lean out the window and shine a flashlight in your direction of travel, both you and the person on the side of the road will measure the speed of light to be the same! This rather non-intuitive result is the basis for the theory of special relativity. It is called “special” relativity because it deals only with the special case of objects moving at uniform velocities (no changing of speed). Once you apply a force to accelerate or decelerate an object, Einstein’s theory of general relativity GR must be used to describe the outcome. More on GR later.

 

Back to Special Relativity. Classical mechanics follows two basic and seemingly intuitive rules defining time and space:

 

1. The time-interval between two events is independent of the relative motion of the reference body.

 

2. The space-interval between two points is independent of the relative motion of the reference body.

 

These sound like gobbledygook. Here are examples to illustrate what they mean.

 

1. Two lightning bolts striking different ends of a moving train are observed by two people equal distance from the train.

    They both observe the strikes at the same exact instant.

 

2. The distance to the star Alpha Centauri is the same for people on Earth and the orbiting space station.

 

 

Einstein showed that neither of these rules is correct.

 

In special relativity, there is no concept of absolute rest. Two space travelers passing each other in their spaceships have no way of telling if either one of them is at rest. They can only know about their relative motion with respect to each other. Consider Galileo’s thought experiment of a cannonball dropped from the crow’s nest of a sailing ship. The person in the crow’s nest sees the ball fall straight, vertically down. But an observer on the shore sees the ball fall at an angle due to the forward motion of the ship. Who is correct? In SR, both are or neither are. It is an irrelevant question.